It seems mathematicians and math teachers struggle to explain how and why 1⁰ = 1 and 1¹ = 1, which might imply 0 = 1.

The reason is truly strange. Whilst 0 and 1 empower computers, (which run on strings of zeros and ones), zero and one have been missing from explanations of multiplication and exponentiation since the 16th Century!

Math teachers appear to be teaching the 'index laws' with no common sense foundations.